Jitter is a measure of the timing variations of logic transitions of digital data signals. The standard practice in high-data rate (e.g., greater than 1 gigabit per second (Gb/s)) serial technologies is to analyze jitter in terms of two sub-components: Random Jitter (RJ) and Deterministic Jitter (DJ). These sub-components are separated from the whole jitter distribution for two reasons. The first reason is to provide a diagnostic tool for debugging circuits. The second reason is to facilitate a quick estimate of Total Jitter measured at a given Bit Error Ratio TJ(BER).
The jitter distribution is closely related to the probability density function (PDF) for finding a particular data transition at some distance from the ideal point. The applied jitter signal is the phase modulation applied to the data pattern that determines the timing position of edges. For example, a sinusoidal applied jitter signal φ(t)=A sin(ωt) yields a jitter PDF (ρ(x)) that follows Equation 1 below:
                              ρ          ⁡                      (            x            )                          =                                            1              A                                                      1                -                                                      x                    2                                                        A                    2                                                                                .                                    Equation        ⁢                                  ⁢        1            
RJ and DJ of a jitter distribution have been separately approximated typically using the double-delta technique (also known as the ‘dual-Dirac’ technique). In the double-delta technique, two key assumptions are made of the RJ and DJ distributions. The first assumption is that RJ follows a Gaussian distribution. A Gaussian distribution is specified by three parameters, its amplitude, width (represented by the standard deviation σ), and mean value (represented by μ). For jitter analysis the key RJ parameter is the width (standard deviation σ of the Gaussian distribution). The second assumption is that the DJ distribution is assumed to be bounded. The double-delta approximation is built on the assumption that any jitter distribution can be quantitatively described as the sum of two Gaussian distributions of not necessarily equal amplitudes or widths. For more information on the double-delta technique, see for example U.S. Pat. No. 6,298,315 and U.S. Pat. No. 6,356,850.